Three-Dimensional Displacement and Strain Measurements by Windowed Phase-Shifting Digital Holographic Interferometry

Abstract

It is important to measure displacement and strain distributions to prevent failures of structures. However, one point measurement method such as strain gage is widely used in industrial practice. It is time–consuming and difficult for one-point method to find the point with the maximum strain on the structures. Whole-field optical methods such as moire method, digital image correlation, speckle method and holography are effective to find the point with the maximum strain (Sharpe, 2008). Especially, holography provides three dimensional displacement information and high resolution. In conventional holography, an object beam and a reference beam interfere each other on a high-resolution photographic plate. It is necessary to develop the photographic plate (hologram) and it is time-consuming and bothersome work. In conventional holographic interferometry, holograms recorded before and after deformation are superposed on a photographic plate and the displacement is obtained from the interference fringe pattern (Valery et al., 1996; Ranson et al., 1993; Hayashi et al. 1986). In digital holography, a hologram is usually recorded on a CCD or C-MOS sensor instead of a photographic plate (Yaroslavskii et al., 1980; Pedriniet al., 1998; Schnars, et al. 2005). In phase-shifting digital holographic interferometry (PSDHI), the complex amplitude of the object is analyzed from the phase-shifted holograms obtained by shifting the phase of the reference beam. The reconstructed image can be calculated from the complex amplitudes of the hologram using the Fresnel diffraction integral with a computer (Yamaguchi et al., 1997; Zhang et al., 1998). The displacement at each point of an object is obtained from the phase-difference between the reconstructed images analyzed from the digital holograms recorded before and after deformation. The equipment is simple and the analysis is fast. It is useful for practical field measurement of displacement and strain distributions. Holograms and reconstructed images have speckle noise and they provide large error in the calculation of displacement and strain analysis. In order to reduce the effect of speckle noise, the authors developed a novel method, i.e., the windowed phase-shifting digital holographic interferometry (Windowed PSDHI). In holography, any part of a hologram has the optical information about the whole reconstructed image. By using this feature of